Bradshaw was commissioned into the Royal Army Medical Corps, British Army, on 9 November 1946 as a lieutenant.[4] He was promoted to captain on 9 November 1947.[5] On 24 November 1948, he transferred from an emergency commission to a short service commission.[6] He spent his early career working in pathology in various United Kingdom based military hospitals and had one short, overseas posting to Sri Lanka.[2] In 1950, he began a two-year posting to the War Office where he worked on laboratory policy.[2] On 26 July 1951, he transferred to a regular commission.[7] In 1952, he began the senior officers' course at the Royal Army Medical College, London.[2] He then qualified as a specialist in pathology.[2] He was promoted to major on 9 November 1954.[8]
In 1954, during the Mau Mau uprising, he was posted to the East Africa Command as a pathologist. During the posting he was also commander of the British military hospital in Nairobi.[2] In 1959, he was posted to Washington, D.C. as an exchange officer. There he worked at the Armed Forces Institute of Pathology.[2] He was promoted to lieutenant colonel on 9 November 1961.[9] From 1963 to 1966, he served as a research pathologist at the Chemical Defence Experimental Establishment, Porton Down.[2] In 1966, he was posted to the headquarters of the British Army of the Rhine as Assistant Director of Pathology.[2] On 9 November 1969, he was promoted to colonel.[10] From 1969 to 1971, he was Professor of Pathology at the Royal Army Medical College.[1]
Following his professorship, his career turned towards command and administration.[2] He served as Commanding Officer of the Cambridge Military Hospital, Aldershot Garrison from 1971 to 1973.[1] On 1 June 1973, he was promoted to brigadier.[11] From 1973 to 1975, he was Commandant of the RAMC Training Centre.[2] He was once more posted to West Germany when, on 6 July 1975, he was appointed Director of Medical Services, British Army of the Rhine and made an acting major general.[12] He was promoted to major general on 26 September 1975.[13] On 30 March 1977, he was appointed Director General Army Medical Services and promoted to lieutenant-general.[14] In the 1977 Queen's Birthday Honours, he was appointed Knight Commander of the Order of the British Empire (KBE).[15]
On 7 April 1981, he retired from the British Army.[16]